Calibration procedures for a computational model of ductile fracture

A recent extension of the Gurson constitutive model of damage and failure of ductile structural alloys accounts for localization and crack formation under shearing as well as tension. When properly calibrated against a basic set of experiments, this model has the potential to predict the emergence and propagation of cracks over a wide range of stress states. This paper addresses procedures for calibrating the damage parameters of the extended constitutive model. The procedures are demonstrated for DH36 steel using data from three tests: (i) tension of a round bar, (ii) mode I cracking in a compact tension specimen, and (iii) shear localization and mode II cracking in a shear-off specimen. The computational model is then used to study the emergence of the cup-cone fracture mode in the neck of a round tensile bar. Ductility of a notched round bar provides additional validation.     

A computational method for quasi-static fracture

A direct method for solving quasi-static, mixed-mode fracture problems is presented. The element-free Galerkin method is used in order to allow for crack growth without remeshing. An expression for the normalized, critical traction is derived in terms of the fracture resistance (R-curve) and a crack-dependent function. Sample problems demonstrate the capability of this method to accurately compute the post-peak equilibrium paths for structures with growing cracks.     

New basis functions and computational procedures for p-version finite element analysis

New basis functions and solution procedures for p-version finite element analysis are described. They are used in a highly efficient p-version finite element solver for linear elastostatics and dynamics, which has been used in an industrial environment for over two years. Using two sample applications it is shown that, using the techniques proposed here, p-version finite element analysis can have a substantially lower computational cost, for given accuracy, than standard finite element methods. This makes the industrial applicability of p-version finite element analysis much wider than is commonly believed.     

On computational methods for variational inequalities

In this note, we focus on optimised mesh design for the Finite Element (FE) method for variational inequalities using global norm estimates for local error control. The strategies are based on the so called dual-weighted-residual (DWR) approach to a posteriori error control for FE-schemes (see, e.g., Rannacher et al. [19, 6, 2]), where error control for the primal problem is established by solving an auxiliary (dual) problem. In this context we blamed (cf. e.g., Rannacher and Suttmeier [18, 19]) global norm estimates being not that useful in applications. But having a closer look at the DWR-concept, one observes that in fact global (energy) error bounds can be employed to establish local error control. Our ideas and techniques are illustrated at the socalled obstacle problem.It turns out, that reliable and efficient energy error control is one main ingredient to establish useful a posteriori error bounds for local quantities. Therefore, in addition, we derive an unified approach to a posteriori error control in the energy norm for elliptic variational inequalities of first kind. Eventually, this framework is applied to Signorinis problem.     

On using different recovery procedures for the construction of smoothed stress in finite element method

The performance of three different stress recovery procedures, namely, the superconvergent patch recovery technique (SPR), the recovery by equilibrium in patches (REP) and a combined method known as the LP procedure is reviewed. Different order of polynomials and various patch formation strategies have been employed in the numerical studies for the construction of smoothed stress fields. Two 2-D elastostatic problems of different characteristics are used to assess the behaviour of the stress recovery procedures. The numerical results obtained indicate that when the order of polynomial used in the recovery procedure is equal to that of the finite element analysis, the behaviours of all three recovery procedures are very similar and all of them are adequate to provide a reliable recovered stress field for error estimation. In case that the order of polynomial of the recovered stress is increased, the LP procedure seems to give a more stable recovery matrix and a more reliable recovered stress field than the REP procedure. © 1998 John Wiley & Sons, Ltd.     

Numerical difficulties and computational procedures for thermo-hydro-mechanical coupled problems of saturated porous media

This paper analyses the numerical difficulties commonly encountered in solving fully coupled numerical models and proposes a numerical strategy apt to overcome them. The proposed procedure is based on space refinement and time adaptivity. The latter, which in mainly studied here, is based on the use of a finite element approach in the space domain and a Discontinuous Galerkin approximation within each time span. Error measures are defined for the jump of the solution at each time station. These constitute the parameters allowing for the time adaptivity. Some care is however, needed for a useful definition of the jump measures. Numerical tests are presented firstly to demonstrate the advantages and shortcomings of the method over the more traditional use of finite differences in time, then to assess the efficiency of the proposed procedure for adapting the time step. The proposed method reveals its efficiency and simplicity to adapt the time step in the solution of coupled field problems.     

A computational method for frictional contact problem using finite element method

Using the finite element method a numerical procedure is developed for the solution of the two-dimensional frictional contact problems with Coulomb's law of friction. The formulation for this procedure is reduced to a complementarity problem. The contact region is separated into stick and slip regions and the contact stress can be solved systematically by applying the solution technique of the complementarity problem. Several examples are given to demonstrate the validity of the present formulation.     

Modified computational scheme of the frontal method

L. I. Lobachevskii Scientific-Research Institute of Mechanics, Gorkii University. Translated from Problemy Prochnosti, No. 7, pp. 94–99, July, 1989.     

Body force method

The body force method is based on the principle of superposition. The solution in the body force method is obtained by the superposition of fundamental solutions so as to satisfy a given boundary condition. By means of these fundamental solutions all problems can be solved in principle. In this paper, first the fundamental principle of the body force method is illustrated and then its application to crack problems, elastic–plastic problems and elastodynamic problems are shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

A finite element method for the computational modelling of cohesive cracks

The present contribution is concerned with the computational modelling of cohesive cracks in quasi‐brittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage‐type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concerning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method. Copyright © 2005 John Wiley & Sons, Ltd.     

An integrated force method for discrete analysis

An integrated force method is developed for the analysis of discrete structures in which all the element forces are taken as the independent variables instead of the conventional way of treating the redundants as the prime unknowns. Computationally the integrated force method is superior to the standard force method. The analogy between Beltrami–Michell formulation for continuous problems and the present formulation for discrete structures is presented. Illustrative examples for the determination of forces and displacements are presented for pin-connected and rigid-connected frame structures for various load conditions.     

动态载荷识别位置优化的传递函数相干法

利用多自由度动力学原理对频域载荷识别方法进行分析,对传递函数病态性进行了研究,分析了动态载荷识别方法中响应点位置对传递函数病态性及载荷识别结果的影响.为降低载荷识别误差特别是结构共振频率下的识别误差,基于传递函数的相干分析定义了传递函数相干因子,并提出以最小传递函数相干因子为目标的动态载荷识别位置优化的传递函数相干法....     

Spiral scanning method for atomic force microscopy

A spiral scanning method is proposed for atomic force microscopy with thoroughgoing analysis and implementation. Comparing with the traditional line-by-line scanning method, the spiral scanning method demonstrates higher imaging speed, minor image distortion, and lower acceleration, which can damage the piezoelectric scanner. Employing the spiral scanning method to replace the line-by-line scanning method, the experiment shows that the time to complete an imaging cycle can be reduced from 800 s to 314 s without sacrificing the image resolution.     

A computational method for inverse free boundary determination problem

Based on the method of fundamental solutions and discrepancy principle for the choice of location for source points, we extend in this paper the application of the computational method to determine an unknown free boundary of a Cauchy problem of parabolic‐type equation from measured Dirichlet and Neumann data with noises. The standard Tikhonov regularization technique with the L‐curve method for an optimal regularized parameter is adopted for solving the resultant highly ill‐conditioned system of linear equations. Both one‐dimensional and two‐dimensional numerical examples are given to verify the efficiency and accuracy of the proposed computational method. Copyright © 2007 John Wiley & Sons, Ltd.     

Meshless method based on orthogonal basis for computational electromagnetics

This paper discovers and researches problems on numerical oscillations of the solution in element-free Galerkin method (EFGM) when it uses high order polynomial basis, and puts forward the meshless method based on orthogonal basis (MLMBOB), which is composed of essential boundary conditions with Penalty method, then gets the numerical solutions of the partial differential equations. This method holds nearly all qualities of EFGM and removes many drawbacks of it, and it has high accuracy when high order orthogonal basis is used. Therefore, it is fit for many problems in engineering computational electromagnetics. Examples are given to prove the proposed method.     

A wavelet method for reducing the computational cost of BE-based homogenization analysis

A wavelet BEM is applied to the evaluation of the effective elastic moduli of unidirectional composites, based on the homogenization theory. This attempt is devoted to the reduction of computational cost for the BE-based homogenization analysis. Truncation for matrix compression is carried out by the Beylkin-type algorithm. A thresholding value for the truncation is set such that the discretization error of BE solution is comparable to its truncation error. Besides, rearrangement of the BE equations is proposed to attain rapid convergence of iterative solutions. Through investigation of asymptotical convergence of the effective moduli, it is found that the BE-based homogenization analysis ensures the same rate of convergence for effective moduli as for characteristic functions. By applying the wavelet BEM to heterogeneous media which have microstructures with many voids, the effective moduli with agreement of 2–4 digits can be evaluated using 20–50% memory requirements of conventional BE approaches.     

On the thermodynamic driving force for coherent phase transformations

Using the basic principles of continuum thermodynamics the notion of the thermodynamical driving force for coherent phase transformations is introduced. The new representations of thermodynamical driving force are derived. It is shown that thermodynamical driving force reaches an extremum at any dynamically admissible phase amplitude, provided that two phase solids exhibit instantaneous elasticity. The possible interpretation of macroscopic thermodynamical driving force for martensitic transformation is presented.